Low heat could be caused by all you mention as well as debris covering part of the core if the screen behind the grill at the front of the air intake is damaged or missing.
As I recall, the air flow thru the core on 51-4 heaters is a bit odd in that flow is split, the air flow only using half the core at a pass. The core lays at a fairly flat angle so air enters thru the bottom and is restricted to half the core at the outside quarters, goes into the upper half of the box and doubles back thru the core to exit into a channel positioned under the core center and then into the car. To my mind air flow and maybe heat output is a bit restricted at only half the core and if debris blocks part of the side entering quarter passes heat would be reduced. At some point they repositioned the core more vertically so air can use the entire area and passes thru just once -- enters one side and exits the other but I think that was not done until the heater assy mounting and inside plenum was redesigned for the 55s.
Aside from something blocking air, any blockage in the core itself that would limit water flow to a portion of the core could also contribute. For valve issues, to rule those out you could always bypass it temporarily and run the heater with full water flow for a few days to see if the heat situation improves.
The cable levers have a compound operation and cable adjustment issues are possible and apparently were known. Packard issued an article on how to check and adjust the dual action levers.
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